(3x+2)(5x-6)=0

Solution for (3x+2)(5x-6)=0 equation:

(3x+2)(5x-6)=0

We multiply parentheses ..

(+15x^2-18x+10x-12)=0

We get rid of parentheses

15x^2-18x+10x-12=0

We add all the numbers together, and all the variables

15x^2-8x-12=0

a = 15; b = -8; c = -12;
Δ = b2-4ac
Δ = -82-4·15·(-12)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-28}{2*15}=\frac{-20}{30}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+28}{2*15}=\frac{36}{30}
=1+1/5
$